On some control problems in fluid mechanics
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The issue of minimizing turbulence in an evolutionary Navier-Stokes flow is addressed from the point of view of optimal control. We derive theoretical results for various physical situations: distributed control, Bénard-type problems with boundary control, and flow in a channel. For each case that we consider, our results include the formulation of the problem as an optimal control problem and proof of the existence of an optimal control (which is not expected to be unique). Finally, we describe a numerical algorithm based on the gradient method for the corresponding cost function. For readers who are not interested in the mathematical details and the mathematical justifications, a nontechnical description of our results is included in Section 5.
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